Use the fact that matrices A and B are row-equivalent. -2 -5 8 0 -17 1 3 -5 1 A = 3 11 -197 1. 1 7-13 5 1 0 -3 1 0 0 1-2 0 3. B 3= 0 0 0 1 -5 0 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
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Answer c and d.

 

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(c) Find a basis for the row space of A.
1 1
(d) Find a basis for the column space of A.
11.1
Transcribed Image Text:(c) Find a basis for the row space of A. 1 1 (d) Find a basis for the column space of A. 11.1
Use the fact that matrices A and B are row-equivalent.
-2 -5
80-17
3 -5 1
A =
3 11 -19 7
1.
1 7-135 -3
10 10
0 1-2 0
B =
0 0
01-5
0 0
0 0
(a) Find the rank and nullity of A.
rank
nullity
(b) Find a basis for the nullspace of A.
Transcribed Image Text:Use the fact that matrices A and B are row-equivalent. -2 -5 80-17 3 -5 1 A = 3 11 -19 7 1. 1 7-135 -3 10 10 0 1-2 0 B = 0 0 01-5 0 0 0 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A.
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